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Attractiveness, variety and interactivity are becoming more and more desirable features of innovation offered in educational projects, systems, models and individual methods, which are described in the theoretical statements of numerous scientific papers proposed in pedagogical literature. The article analyzes the practical importance, opportunities and challenges of implementing new, unconventional ideas based on animation practices in education. The issue of the effectiveness of the animation projects based on the educational drama model in elementary school and its practical dimensions, important for non-formal education, is raised.
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On the basis of the natural connections between the science and mathematics, an interdisciplinary approach is applied in the non-formal chemistry classes of the Sofia High School of Mathematics. The 7th grade students have pronounced mathematical ability and the teacher is competent in chemistry and mathematics. In this case chemistry and mathematics are integrated both on the basis of content and procedural level. Seventh graders apply their mathematical knowledge and skills in acquisition of new chemistry knowledge. They solve problems and develop projects, requiring integration of both subjects. In this way, students form complex communication, problem-solving and systemic thinking skills. As a result of the approach used, students develop their talents and abilities, increase their interest in science, and improve their achievements at the Olympiads in Chemistry.
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By using the computer program “Discoverer” we find 85 different geometric constructions of Malfatti squares. Of them 79 are new constructions, and the other 6 are old constructions.
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Examples are shown in the present paper about the realization of interdisciplinary connections between trigonometric functions and progressions in high school mathematical curriculum.
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The paper is an elaboration by high school students under the scientific advices of Assoc. Prof. Dr. Veselin Nenkov. The new results in it were estimated highly during its presentation at the International competition “Methodology and Information Technologies in Education” in 2018 and the work was awarded first prize. It is dedicated to a well-known problem for triangle and quadrilateral areas determined by triangle secants. A general formula is found for the area of one of the triangles. The areas of triangles are determined when obtained by isotomic and isogonal transformations in the plane of a given triangle. What is investigated is the question for equal areas of the obtained triangles and the generating ones.
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The motivation behind this project generated in the classes I attended as an undergraduate student; these classes inspired me to get more closely involved with the poetry of Miltos Sachtouris, on a much deeper level. In the context of the class devoted to “Bulgarian Literature and Cultural Review” (this lesson was taught by Mrs. Stefania Filipova-Metzimeki) in our postgraduate program of the Department of Balcan, Slavic and Oriental Studies“ History, Anthropology and Culture in Eastern and South- eastern Europe” I decided to indulge in the color motive within the poetry of M. Sachtouris, and – comparatively – within the poetry of Kiril Kadiisky. So that I could better understand the latter, I have studied the one and only study I managed to discover, written in French. Yet, it proved to be more than helpful in understanding some quite important meanings in his poetry As for the poetry of M. Sachtouris, the number of the available sources was quite large. Still, I was not interested in recycling the already existing projects.
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The purpose of this article is to show that there are no age limits for the use of dynamic mathematical software. There are no limitations on how to use it and the depth of the results. The only limitation lies in the capabilities and imagination of those who use it.
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Exemplary applications are considered in the paper in connection with the mathematical curriculum of high school mathematics education. The proposed problems are in the format of PISA and form skills for modeling different situations.
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A model is proposed in the paper to solve linear equations with the help of Excel. The solutions of the equations are found on the base of coefficients from the trend line. Work with ordinary fractions is introduced by not complicated automations. A practical experience of the model application is shared.
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The paper considers the proofs of two interesting geometric inequalities for acute triangles.
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In comparison with (Grozdev, Okumura. & Dekov, 2018) an alternative construction of Malfatti squares is presented.
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It is considered a transformation in the plane of a quadrilateral, allowing to obtain generalizations of the well-known lines of Gauss and Gauss-Bodenmiller for the complete quadrilateral.
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The paper is an elaboration of a high school student under the supervision of Assist. Prof. Stanislav Stefanov. It was awarded first prize in the National round of the International Competition “Methodology and information technologies in Education in February, 2018. Some basic results from the geometry of the quadrilateral are systemized and presented in connection with two new transformations in the plane of a quadrilateral that have important applications in the geometry of the quadrilateral. The main of the applications are generalizations of the theorems of Miquel, Gauss and Gauss-Bedenmiller for the complete quadrilateral and the accompanying assertions. The transformations in question serve also in proving geometric relations among the newly found notable points in the plane of a quadrilateral and in deducing properties of some of them and properties of others that are images of the first ones after being transformed. None the less, that they have heterogeneous definitions, the two transformations are connected narrowly. One of them turns to be a diffusion of the other from a determined set of points in the plane of a given quadrilateral to the whole plane.
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The so called “symmetric” numbers are considered in the paper and the authors study some of their various properties. Several interesting questions and problems for numbers of that kind are formulated and some concrete examples are solved. Corresponding generalizations of them are proposed. The investigation could be a base for creating many other problems, which could be used in mathematical Olympiads and competitions, as well as for the preparation for them.
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The study is dedicated to the range of didactic games in History education. There are seven methodical approaches: “Bluff Club”, “Business Cards”, “Historic Maritime Chess” (“Noughts and Crosses”), “Mnemotechnics”, “Determining the Location”, “Spy-Scouts” and “Three Directions”. The recommendations are suggested for their preparation and conduct. The examples used are in line with new curricula and textbooks on the History and Civilizations subject.
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The article presents an NDM taxonomy systemizing the pedagogical aims of the relationships in the dyad “Individuality – Personality”. These pedagogical aims lead to optimistic innovative processes defining learning as a manageable object linked with the development of the noospheric intellect. The focus is on two main learning environments (a thought-developing environment and a thought-mastering environment) because of the fact that the process of thinking lies in the heart of the optimal development of the treated dyad Individuality – Personality.
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The present article shows development of a model for solving linear equations with Excel. New technique is introduced for the examination of domains.
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It is considered a geometric relation between a polynomial with collinear roots and the roots of its derivative by means of a special ellipse, which is generated by the roots of the polynomial.
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Annotations of two new dissertations of PhD students are presented. Both of them are in the domain of methodology of Informatics education and are defended successfully in Plovdiv University “P. Hilendarski”.
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